The court document specifically laid out the provisions based on Koranic law. My concern is.. will the next step be similar decisions to settle domestic disputes? I'm looking at this from the "camel's-nose-in-the-tent" context.
No, the motion to enforce specifically laid out the enforcement provisions established by the private arbiter, per the terms of the contract that stipulated all contract disputes be resolved by private arbitration.
Everyday, judges in America enforce private arbitration awards that were based on "law other than US". If you're doing contractual business with a large, German firm - BMW for instance - I promise you that there will be elements of that contract that stipulate German law, not American law be applied. And, from contract disputes growing from those contracts, US judges have enforced not only private arbitration awards based on German law, but they've actually litigated in the courts these German provisions because private arbitration isn't always stipulated. Does that mean German law is "the camel and his curious nose"? No, of course it isn't.
"My concern is.. will the next step be similar decisions to settle domestic disputes?"
Well, if by "domestic dispute" you mean divorce, then that is entirely possible. If the married couple have signed a pre or post nuptial agreement that stipulates some Koranic law apply, then that Koranic law will (perhaps) at least partially apply.
Mega-rich people who have prenuptial agreements will often include a choice of law clause that stipulates a specific state's law will apply in their divorce proceeding, irrespective of where that divorce is actually litigated. For example, people who were married in NYC, but divorced in California could have their California divorce litigated by a California judge who (following the terms of the prenup) is applying Florida law (FL is a popular state to choose). Does that mean California law is being "infected" by FL law? No, of course not.